U.S. patent number 6,816,434 [Application Number 10/079,219] was granted by the patent office on 2004-11-09 for seismic detection.
This patent grant is currently assigned to ABB Offshore Systems Ltd.. Invention is credited to Robert Hughes Jones.
United States Patent |
6,816,434 |
Jones |
November 9, 2004 |
Seismic detection
Abstract
A method of using a seismic detector including four seismic
sensors having axes which are in a substantially tetrahedral
configuration, each of the sensors being in a respective signal
channel, includes one or more of the following steps: combining
outputs from the sensors to check that their polarities are
correct; testing to ascertain if one of the sensors is not working
and, if so, using the outputs from the other three sensors to
obtain an indication of motion in three dimensions; if all four
sensors are working, using their outputs to obtain an indication of
motion in three dimensions on a least squares basis; checking that
the outputs from the sensors are coherent; and checking the gains
(or sensitivities) of the four channels.
Inventors: |
Jones; Robert Hughes (Falmouth,
GB) |
Assignee: |
ABB Offshore Systems Ltd.
(GB)
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Family
ID: |
9909537 |
Appl.
No.: |
10/079,219 |
Filed: |
February 19, 2002 |
Foreign Application Priority Data
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Feb 26, 2001 [GB] |
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0101744 |
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Current U.S.
Class: |
367/13;
73/1.85 |
Current CPC
Class: |
G01V
1/16 (20130101) |
Current International
Class: |
G01V
1/16 (20060101); G01V 001/18 (); G01V 013/00 () |
Field of
Search: |
;367/13 ;73/1.82,1.85
;181/401 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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266183 |
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Sep 1982 |
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DE |
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2275337 |
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Aug 1994 |
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GB |
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WO 01/99028 |
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Dec 2001 |
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WO |
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Primary Examiner: Lobo; Ian J.
Attorney, Agent or Firm: Barnes & Thornburg
Claims
What is claimed is:
1. A method of using a seismic detector including four seismic
sensors having axes which are in a substantially tetrahedral
configuration, to detect and measure seismic activity, each of the
sensors being in a respective signal channel, the method including
the step of checking the gains of the four channels by taking a
plurality of samples from the sensors, constructing a set of
simultaneous equations from the samples, and solving the equations
to determine the gains of the four channels.
2. A method of using a seismic detector including four seismic
sensors having axes which are in a substantially tetrahedral
configuration, to detect and measure seismic activity, each of the
sensors being in a respective signal channel, the method including
the following steps: a) combining outputs from the sensors to check
that their polarities are correct; b) testing to ascertain if one
of the sensors is not working and, if so, using the outputs from
the other three sensors to obtain an indication of motion in three
dimensions; c) if all four sensors are working, using their outputs
to obtain an indication of motion in three dimensions on a least
squares basis; d) checking that the outputs from the sensors are
coherent; and e) checking the gains of the four channels.
Description
BACKGROUND OF THE INVENTION
(1) Field of the Invention
The present invention relates to seismic detection, for example to
seismic detection carried out down a bore-hole to detect and
measure seismic activity as represented by particle velocity or
particle acceleration.
(2) Description of Related Art
It is already known to use, for such purposes, seismic detectors
which have sensors oriented along three axes preferably at right
angles to one another.
However, in such a detector, using three axial sensors, if one
sensor (or the electronics associated with it) should fail, then
the resulting two-component detector cannot give a representation
of the three-dimensional movement which it is attempting to
measure. Only a two-dimensional projection of this
three-dimensional motion on to a plane can then be measured.
Also, the margin of error in such a three-axis detector is
considerable since the `error inflation factor` (i.e. the
relationship between the error propagated from the measurement to
the final estimate) is substantially 1 for each axis of a
three-component system which means that for such a system the
errors are compounded in the final estimates.
Moreover, there is no scope for cross-checking in such a three-axis
detector. GB-A- 2 275 337 describes a seismic detector comprising a
sonde which includes a configuration of four sensors (typically
accelerometers or geophones) mounted in an equi-angular tetrahedral
configuration with respect to one another to deal with the above
problems. The four-sensor arrangement provides for some redundancy
in the system such that the failure of one sensor still allows
particle motion to be reconstructed in three dimensions (3D) and
furthermore some form of error determination can be made, neither
of which can be effected by the conventional three-sensor system.
However, there is no disclosure of the processing required to
realise these advantages, nor the processing required to extract
the required seismic information from the configuration.
BRIEF SUMMARY OF THE INVENTION
According to the present invention, there is provided, a method of
using a seismic detector including four seismic sensors having axes
which are in a substantially tetrahedral configuration, each of the
sensors being in a respective signal channel, the method including
one or more of the following steps: a) combining outputs from the
sensors to check that their polarities are correct; b) testing to
ascertain if one of the sensors is not working and, if so, using
the outputs from the other three sensors; c) if all four sensors
are working, using their outputs to obtain an indication of motion
in three dimensions on a least squares basis; d) checking that the
outputs from the sensors are coherent; and e) checking the gains
(or sensitivities) of the four channels.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a flow chart diagrammatically showing the steps of the
present inventive method;
FIG. 2 is a display of data representing a typical microseismic
event;
FIG. 3 is a display of the same data as FIG. 2, after the
transformation of four sensor data to provide three orthogonal
traces;
FIG. 4 is a display of the same data as FIG. 2, except that the
vertical signal has been halved before the transformation was
performed;
FIG. 5 is a display of data similar to that shown in FIG. 4, where
the polarity of the vertical has been changed; and
FIG. 6 is a display of data showing application of the gain
recovery procedure of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
There will now be described an example of the present invention,
namely the processing steps using a seismic detector including four
tetrahedrally arranged sensors, each sensor being in a respective
signal channel which could include an amplifier receiving the
sensor's ouput. It should be noted that the conventional orthogonal
sensor arrangement does not allow any of these processing steps.
The processing steps include one or more of the following
steps.
1. Simple Polarity Checks
As there are more components than unknowns, combining them allows
checking that the polarities of the sensors are correct. This is
simply done by adding the outputs from the four sensors. When all
the sensors are working correctly, the four outputs will add to
zero because of the geometry of the sensors. This process cannot be
applied in a conventional three-sensor configuration because, by
definition, if sensors are orthogonal, then no cross-checking can
be performed.
2. Single Component Failure
If any one of the sensors, fails it is possible to still
reconstruct the full 3D-particle motion with around 80% of the
reliability of a three-sensor orthogonal set. This is possible
because the three remaining sensors still span the three
dimensions, although they do not do so as efficiently as three
orthogonally arranged sensors.
3. Least Squares Optimum 3D Particle Motion
The four-sensor configuration is over-determined. This means that
there are more measurements than there are unknowns. The
three-sensor orthogonal arrangement is an even-determined system,
as there are the same number of readings as unknowns. For the
four-sensor configuration, a "least squares" estimate of each
reading can be formed. This is more accurate than just the single
estimate that a 3-sensor system allows.
4. Four Component Coherency
For each time sample four readings are made for three unknowns,
which means that it is over-determined, i.e. four data points and
three unknowns. By making a least squares estimate of the signal
values, a type of root mean square (rms) is formed for the signal
misfit. The normalised misfit is termed the four-component
coherence (4CC). When all the sensors are working correctly and a
signal, which is large compared to the system's noise, is measured
then the 4CC, or normalised rms, will tend to zero. This allows the
system to be checked and can also be used to measure the onset of
transient signals.
When no signal is present, but only incoherent noise, then the
normalised rms is large. When a signal arrives, the four sensors
give a coherent signal and the normalised rms becomes very small.
As the signal fades back towards the level of the background noise,
the normalised rms increases and so can be used as an objective
measure of signal to noise. The 4CC allows checking that all the
sensors are functioning properly and so a quality check of the data
on a sample-by-sample basis.
5. Gain Recovery
If the gain of one or more of the sensor channels has changed over
time, it is possible to regain a least squares best estimate of the
gains and so adjust the gains over time. As described above, the
simple summing of the channels will, in the presence of a coherent
signal, give an answer of zero. This process can be repeated for
many samples and a set of simultaneous equations constructed where
the unknowns are the relative gains of the four channels. There are
two possible solutions of such a set of equations. The first
solution, which always exists, is that all the gains are zero. If
this is the only solution that exists, then this is interpreted as
meaning that the gains are changing rapidly with time, i.e. the
sensors and/or their amplifiers are not working correctly. The
second solution gives the best least squares estimate of the
relative gains of the channels. This estimate can then be used to
reset the relative gains of the channels if they are found to have
drifted 1 over time.
The above processing is shown diagrammatically as a flow chart in
FIG. 1.
The mathematics typically required to effect the processing steps
above is described as follows.
In the interests of clarity, some simplifications have been made.
Firstly, as it is the configuration of the sensors rather than
their response functions that is being analysed, it is assumed that
they have perfect impulse responses. The reference frame is defined
such that the axes are aligned with the sensors. In the case of the
four-sensor tetrahedral configuration, a first sensor is aligned
with the z-axis, a second is aligned in the x=0 plane and the
remaining two sensors are arranged so that all the sensors have
equal angles between them. The configuration may be as in GB-A- 2
275 337.
The recording situation for an orthogonal three-sensor detector can
be written as: ##EQU1##
where Xr, Yr and Zr are the positional values of the particle
motion in the earth and Xo, Yo and Zo are the positional values of
the particle motion of the observed on the X, Y and Z sensors
respectively. Equation (1) shows the recording situation as it is
normally assumed to exist. More explicitly this may be written out
as: ##EQU2##
or in matrix form:
Once the problem is posed as in equation (2), it can be regarded as
a trivial linear inverse problem. The inverse of the matrix A in
equation (3), which is the identity matrix, is also the identity
matrix. However in some cases the situation will not be this simple
but is more likely to be: ##EQU3##
where E, F and G are unknown although they are likely to be around
one (or minus one if the detector is wired incorrectly). It can be
seen that if E, F and G are not all unity, the inverse of the
matrix A is not the identity matrix. For the tetrahedral
four-sensor detector configuration, the situation is different. Now
the linear inverse problem is over-determined, as there are four
equations and only three unknowns. The equation can be written as:
##EQU4##
In equation (5) it can be seen that there are four observations
(Ao, Bo, Co and Do) and three unknowns (Xr, Yr and Zr). The system
is over-determined and as well as producing an estimate of the
three unknowns, an estimate of the uncertainty (or error) can also
be calculated.
Solving equation (5) using the generalised inverse (Menke, 1981)
gives: ##EQU5##
The singular value decomposition (SVD) method is used to derive
condition number and singular values for equation (5). Properties
of the matrix which are worthy of note are that, as with equation
(2), the condition number is 1.0 but now the singular values are
all 1.1547 rather than 1. This means that the final least squares
estimates of Xr, Yr and Zr are more reliable than the individual
measurements. The uncertainty in the values is reduced by a factor
of 1.15.
One Sensor Failure
The effect of a single sensor failing for the case of the three-
and four-sensor configurations is now considered. For the
three-sensor orthogonal configuration, the failure of a single
sensor means that the 3D particle motion is lost. However, this is
not the case for the four-sensor tetrahedral configuration.
Considering equation (5), if to be concrete we let the receiver D
fail, Equation (5) can now be written as:
Active components: ##EQU6##
Failed component:
The three by three matrix A now has the generalised inverse
##EQU7##
The very existence of (8) means that the 3D particle motion can be
reconstructed even when any one of the four sensors fails. For the
tetrahedral configuration with one failed sensor, one of the
singular values is reduced to 0.577 and the condition number
increases to 2. The uncertainty in the estimated signal is now
increased by 1.732. In other words, the estimated uncertainty is
now twice that of the full tetrahedral configuration.
Four Component Coherence
As has been shown in the previous section, the four-sensor
configuration means that,the signal estimate of the 3D particle
motion is a least squares estimate and the results form an
over-determined system of equations. Incoherent and coherent
signals can be distinguished from each other. This means that, for
the four-sensor configuration, a residual, or misfit, can also be
calculated. If all the signals of all the sensors agree, then this
misfit will be zero. This ideal is approached when all the sensors
are working properly and a strong signal is detected on all the
sensors, i.e. the signal to noise ratio is high. If, on the other
hand, only random signals are detected on the four sensors or a
sensor does not work correctly, then the misfit or residual will
not be zero. Thus the normalised misfit, or one minus the
normalised misfit, which is here termed 4CC coherency, is a useful
measure of signal quality. The over-determined nature of the
configuration can therefore be used to distinguish between
incoherent and coherent signals.
In matrix form we write:
where the matrices are as defined in equation (5), then:
where b is the expected value resulting form the least squares
estimate. Substituting into (7) gives:
which simplifies to: ##EQU8##
It can be seen that the misfit is simply calculated by just adding
the four recorded signals. The 4CC for the n.sup.th sample is then
defined as:
Some examples of 4CC and its uses will now be illustrated.
FIG. 2 shows a typical microseismic event. The time scale is in
milliseconds and the amplitudes are given in micro-g. Clear p-wave
and s-wave arrival can be seen in FIG. 2 and are marked by upward
pointing triangles below the traces. FIG. 3 shows the same data as
FIG. 2 but now the four-sensor data has been transformed using
equation (5) to give three orthogonal traces and the bottom trace
is now the 4CC as defined by equation (1 5). Several features of
the coherency are worth comment. The 4CC increases from around zero
to one at the point the p-wave arrives. Thus 4CC can be used to
help in accurate phase detection. The 4CC can be seen to reduce
gradually toward the end of the trace, this giving some measure of
the signal to noise ratio of the signal.
FIG. 4 shows the same data as FIG. 2 but now the signal on the
vertical has been halved before the transformation was performed.
Comparison of the bottom trace on FIGS. 3 and 4 show the effect
this gain mismatch has on the 4CC. The analyst is alerted to the
fact that the data are not within calibration, which stops the data
being misinterpreted, e.g. polarisation analysis would produce
erroneous direction estimates.
FIG. 5 shows a similar case to that illustrated in FIG. 4 but now
the polarity of the vertical has been changed. This is the same as
multiplying the gain by minus one. Again, the effect on the 4CC is
easily seen and corrective action can be taken.
Gain Recovery
It is a property of the tetrahedral four-sensor configuration that,
at any given time, the sum of the signals on the four sensors
equals zero (Equation 5) when the signal is coherent, i.e. when the
signal to noise ratio is large. This provides a useful way of
checking the performance of the system and recovering the gains or
sensitivities of the sensor channels if they have changed from
their initial values.
A simple set of linear equations can be set up for a trace with the
four fixed but unknown gains (G1, G2, G3 and G4) of the sensor
channels for samples 1, 2, 3, 4, etc. written as: ##EQU9##
for samples 1 to n. This can be re-written in matrix notation
as:
where the matrix A consists of the measured traces and x the four
fixed but unknown gains or sensitivities.
This system of equations is known as a set of homogeneous
equations. Homogeneous equations have either one or two solutions.
The first solution, the trivial solution, which always exists is
x=0. For the four-sensor configuration, this can be interpreted as
the gains all being zero. The second solution, the non-trivial
solution, can only exist under the condition that A is rank
deficient. For real data, A will not be perfectly rank deficient
but may be close to rank deficient. Singular value decomposition
can be applied to the matrix A to analyse it. If the matrix A is
found to be rank deficient, then the relative gains may be
optimally recovered. However, it should be noted that only the
relative values of the gains may be recovered. The total gain of
the four-sensor channels may be normalised or one gain may be
arbitrarily taken as being correct.
Singular value decomposition also has the advantage that the
condition number of the matrix A is given and this indicates how
close, numerically, the matrix A is to being rank deficient. Not
only does the technique allow the recovery of the gains, but the
suitability of the data to this type of analysis is also given.
Hence if the gains are varying rapidly with time the analysis will
show this and stop the user being misled. FIG. 6 shows the
application of the gain recovery procedure described in the
preceding paragraphs and how it affects the 4CC. The top trace
shows the 4CC for the original data. The middle trace shows the 4CC
after the gain of one of the traces is halved. The bottom trace
shows the 4CC after the application of the gain recovery procedure
using the homogeneous equation approach. The gains are recovered to
within 5 percent of their original values for these data.
Summary of Process Achievements (1) Sensor redundancy. The
configuration is robust and, even if a sensor fails, the full three
dimensional particle motion can be recovered. (2) 4CC allows for
signal quality to be assessed objectively and sensor malfunctions
to be easily detected. (3) 4CC aids in the accurate picking of
p-wave phases. (4) Unknown gains or changes in sensitivity can be
accurately recovered while the instruments are still in situ and
without recording being interrupted.
It is emphasised that the mathematics described above is an
illustration only of a method of achieving processing steps
according to the invention.
It will be appreciated that the processing steps may be carried out
by data processing means using software or by hard-wired logic, for
example.
Another aspect of he present invention is the addition to the
four-sensor detector of an omni-directional hydrophone to remove
the ambiguity of a received wave being in compression or dialation
in any seismic event.
* * * * *